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Supercooled water isn't quite the same thing you're asking for - I doubt it could be done with a shower without special equipment - but here's a video of spontaneous freezing in two ways: https://www.youtube.com/watch?v=Fot3m7kyLn4

The first, pounding it inside the sealed bottle, is creating some sort of disturbance to crystalize around (an "unsuspecting nucleus"), and the second is pouring it semi-shower-like.

A shock would likely cause a nucleus site anyway. When people do this with water in the freezer a good knock sets it off. So when the water starts to flow I think it'd freeze in the pipes.

High pressure would probably be a more likely explanation for a shower. As for the feasibility... we're talking about technicalities here.

I do think it would be interesting to see it, though.